Quantum field theory on noncommutative spaces
Abstract
A pedagogical and self-contained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the Weyl-Wigner correspondence, noncommutative Feynman diagrams, UV/IR mixing, noncommutative Yang-Mills theory on infinite space and on the torus, Morita equivalences of noncommutative gauge theories, twisted reduced models, and an in-depth study of the gauge group of noncommutative Yang-Mills theory. Some of the more mathematical ideas and techniques of noncommutative geometry are also briefly explained.
- Publication:
-
Physics Reports
- Pub Date:
- May 2003
- DOI:
- 10.1016/S0370-1573(03)00059-0
- arXiv:
- arXiv:hep-th/0109162
- Bibcode:
- 2003PhR...378..207S
- Keywords:
-
- High Energy Physics - Theory;
- Condensed Matter;
- General Relativity and Quantum Cosmology;
- High Energy Physics - Lattice;
- High Energy Physics - Phenomenology;
- Mathematical Physics;
- Mathematics - Quantum Algebra
- E-Print:
- 111 pages LaTeX, 6 eps figures